Quantizing superstrings in AdS/CFT, perturbatively and beyond

String sigma-models relevant in the AdS/CFT correspondence are highly non-trivial two-dimensional field theories for which predictions at finite coupling exist, assuming integrability and/or the duality itself.  I will discuss general features of the perturbative approach to these models, and present progress on how to go extract finite coupling information in the most possibly general way, namely via the use of lattice field theory techniques. I will also present new results on certain ``defect-CFT’' correlators  at strong coupling.